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Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago

A tangent and a secant x = ?

guajiro [1.7K]

x = 45°

Solution:

Given data:

Measure of larger arc = 152°

Measure of smaller arc = 62°

<em>If a tangent and a secant intersect at the exterior of a circle then the measure of angle formed is one-half the positive difference of the measures of the intercepted arcs.</em>

$$\Rightarrow x = \frac{1}{2}(\text{ larger arc }- \text{smaller arc} )$

$$\Rightarrow x = \frac{1}{2}(152^\circ-62^\circ)$

$$\Rightarrow x = \frac{1}{2}(90^\circ)$

⇒ x = 45°

The value of x is 45°.

8 0

3 years ago

If 15% of x is 42, what is x?

Blizzard [7]

Answer:

x=280

Step-by-step explanation:

We have, 15% × x = 42

or,

15

100

× x = 42

Multiplying both sides by 100 and dividing both sides by 15,

we have x = 42 ×

100

15

x = 280

If you are using a calculator, simply enter 42×100÷15, which will give you the answer.

6 0

3 years ago

Read 2 more answers

What is the averge of 70 and 93?

pychu [463]

Add 70+93, then divide by the number of numbers, which is 2.
70+90=163
163/2=81.5
Hope this helps!

3 0

3 years ago

Read 2 more answers

1. Denise makes 21 quarts of ice cream. She stores the ice cream in containers

Mkey [24]

Answer:

21 containers

Step-by-step explanation:

21/1=1

4 0

3 years ago